Theorems · Theorem · group theory
Subgroup.comap_injective
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N},
Function.Surjective ⇑f → Function.Injective (Subgroup.comap f)- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.comapstatement · cited by 154
- Subgroup.comap_le_comap_of_surjectiveproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Group.nilpotencyClass_quotient_centerproof · cited by 3
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- Group.normalizerCondition_of_isNilpotentproof · cited by 2
- Subgroup.isCoatom_comap_of_surjectiveproof · cited by 1
- IsSimpleGroup.isSimpleGroup_of_surjectiveproof · cited by 1
- Subgroup.normal_comap_iff_of_surjectiveproof · cited by 1